4984
Aiken, S . C., operated by E. I. du Pont de Nemours and Co., under Contract No. AT(07-2)-1 with the U. S. Atomic Energy Commission. We wish to thank Dr. John A. Stone of the Savannah River Laboratory for his assistance with the low-temperature measurements, and Professor R. L. Belford for valuable discussions.
routinely carried out for SCF plus single excitations only. We carried out a much more exhaustive geometry search than previous ab initio investigator^^^^*^ of CH2. The calculated total energies from our largest calculation (including 408 3B1 configurations) are given as a function of geometry in Table 1. Our lowest calculated
(20) (a) Address correspondence to this author; (b) NDEA Title IV Fellow, 1966-1969; (c) NSF Trainee, 1968-1970; (d) ORAU Research Participant at the Savannah River Laboratory, Aiken S. C., during the summer of 1969.
Table I. Calculated A b Initio Energies for the Ground 3Bj State of C H p
William E. HatReld,aa James A. Barnesab David Y. Jeter,”c Robin Whyman Department of Chemistry, University of North Carolina
e 90” 105’ 120” 135” 150” 165” 180O
Chapel Hill, North Carolina 27514
Edwin R. Jones, Jr.”d Department of Physics, University of South Carolina Columbia, South Carolina 29208 Received April 4 , 1970
New Theoretical Evidence for the Nonlinearity of the Triplet Ground State of Methylene Sir: It is generally accepted’ that the triplet ground state of the CH, molecule is linear. However, it is interesting to note that both Walsh,2 in his early qualitative paper, and Herzberg, in his experimental study, leave open the possibility that this state is “nearly linear.” Further, early ab initio configuration interaction (CI) calculations by Foster and Boys4 indicated a relatively flat surface with changing angle and an equilibrium angle of 129’. Finally, from recent valence-bond calculations, Harrison and Allen5 predicted an angle of 138” for the ground 3B1state. We have recently begun a relatively accurate series of quantum mechanical calculations on the low-lying states of the CH2 radical. It was decided to first investigate the question of the geometry of the ground state. The gaussian basis functions used in this work were Huzinaga’s69s,5p set for carbon and 4s set for hydrogen. The functions were contracted to 4s,2p for carbon and 2s for hydrogen (with a scale factor of 1.2), according to Dunning’s recommendation^.^ The first step in each calculation involved the computation of the SCF wave function within the above basis. Then CI calculations were carried out including the SCF function (la12 2a12 lbZ23al lbl in this case) plus all configurations of 3B1symmetry arising from orbital occupancies differing by one or two orbitals from the SCF function, with the restriction that the lal orbital was always doubly occupied. An iterative natural orbital procedure* was then used in several subsequent C1 calculations to obtain the most rapidly convergent expansion of the above type. Calculations were also (1) G. Herzberg, “Electronic Spectra of Polyatomic Molecules,” Van Nostrand, Princeton, N. J., 1967. (2) A. D. Walsh, J . Chem. SOC.,2260 (1953). (3) G. Herzberg, Proc. Roy. Soc., Ser. A, 262, 291 (1961). (4) J. M. Foster and S. F. Boys, Rev. Mod. Phys., 32, 305 (1960). (5) J. F. Harrison and L. C. Allen, J . Amer. Chem. Soc., 91, 807 ( 1969). --
R, bolus 2.0
1.9
- 38.92913 - 38,94283 - 38.95363 - 38.96588 - 38.96644 - 38,97761 - 38.97045 -38,98077 - 38.96881 - 38,97838 - 38.96527 - 38,97413 - 38.96347 -38,97200
2.1
2.2
- 38.94751 - 38.96916 - 38.97986 -38.98222 - 38.97912 - 38.97425 -38.97184
- 38.94554 - 38,96583 - 38.97554 -38.97717 - 38,97344 - 38.96799 -38,96530
a The wave functions were of the configuration-interaction variety, including the SCF function plus all singly and doubly excited configurations arising from a “double-r’ gaussian basis set. In all, 408 configurations were included.
total energy lies 0.0671 hartree = 42 kcal/mol below the lowest energy previously reported, that of Harrison and Allen.5 Force constants were obtained by fitting the expressionlo 2V
= Fllr12
+ F22r22iFa3R2a2
where r1 and r2 are the stretches of the two CH bonds, CY is the distortion of the equilibrium bond angle, and R is the equilibrium bond length. Table I1 gives the predicted geometry and force constants for each of the three types of calculation carried out. Table 11;
Predicted Equilibrium Geometry and Force Constants (mdyn/A) of CHQ
SCF
+
SCF
+
single excitations
+
SCF single ex- double ex- Expericitations citations menta
~~
Bond distance, A Bond angle, deg Interpolated total energy, hartrees Fii = Fzz F3 3 a
1.080 1.080 129.8 135.7 - 38.913 - 38.921 6.41 0.26
6.52 0.20
1.096 1.03 135.1 180 - 38.984 6.83 0.21
See ref 3.
All the present calculations indicate that the methylene ground st!te is bent, with a bond distance greater than the 1.03 A determined by Herzberg.3 In light of the present results it is interesting to note that an alternate interpretation3 of Herzberg’s ospectroscopic data suggested a bond distance of 1.071 A and a 140’ angle, in good agreement with our predictions. However, owing to the absence in the spectrum of certain subbands, Herzberg3 concluded the above geometry to be unlikely. The fact that the potential surface is rela-
\ - -
(6)’s. Huzinaga, J. Chem. Phys., 42, 1293 (1965). (7) T. H. Dunning, manuscript in preparation. (8) C. F. Bender and E. R. Davidson, J . Phys. Chem., 70,2675 (1966).
Journal of the American Chemical Society
(9) M. Krauss, J . Res. Nat. Bur. Stand., Sect. A, 68, 635 (1965). (10) E. B. Wilson, J. C. Decius, and P. C. Cross, “Molecular Vibrations,” McGraw-Hill, New York, N. Y., 1955, p 170.
/ 92:16 / August 12, 1970
4985
tively flat in going from 135 to 180’ may make a rigorous experimental determination of the geometry rather difficult. Oyr most stable calculated linear geometry (r = 1.083 A) lies only 6.7 kcal/mol above the calculated equilibrium geometry. Nevertheless, on the basis of the present and p r e v i o ~ sab ~ , initio ~ calculations and the stated experimental uncertainties, we conclude that the CH2 grou!d state is nonlinear with a geometry close t o r = 1.096 A, 0 = 135.1O. Since there is a great deal of current interest” in rapidly convergent CI expansions for molpdes, Table I11 includes the seven most important spatial Table III. The Seven Most Important Spatial Configurations in the Natural Orbital Expansion of 3B1 CHz at 0 = 135”, r = 2.1 bohra Excitation
Spatial configuration
Coefficient
1. 2. 2al lbz -,4al 2bz 3. 2al -,4al 4. lbz’+ 2bz2 5. lbzZ -+ 4aI2 6. 2 a 1 2 -+ 4a12 7. lbz lbl -+ 2bz 2bl
1alZ2a12l b z 23al lbl 1aI22a1 lbz 3al lbl 4al 2bz l a l a 2al l b z 23al lbl 4al l a I 22al23al lbl 2bS2 laI2 2 a 1 2 3al lbl 4a12 la12 lbz2 3a1 lbl 4aI2 la12 2al2 lbz 3al 2b 2bl
0.97914 0.07269 0.06393 0.05686 0.05246 0.05027 0.04725
The coefficients incorporate the effects of all triplet spin eigenfunctions corresponding to the given orbital occupancy.
configurations in our natural orbital expansion near the minimum. We note that (1) all of these configurations involve only valence orbitals, (2) the SCF configuration dominates, (3) the second most important orbital occupancy involves six electrons outside closed shells, and (4) the single excitation 2al + 4al is very important. (11) G. Das and A. C. Wahl, J . Chem. Phys., 44, 87 (1966). (12) (a) Supported by a grant from the Chemical Applications
Department of the UCC Computer Utility Network; (b) supported in part by the Petroleum Research Fund and the Research Corporation; to whom correspondence should be addressed. Charles F. Benderlla University Computing Company Palo Alto, California 94306 Henry F. Schaefer I I I 1 2 b Department of Chemistry, University of California Berkeley, California 94720 Received June 3, 1970
Vinyl Cations from Solvolysis Sir: In a recent communication Schubert and Barfknecht commented regarding the solvolyses of vinyl halides which are proposed to occur by the SN1 mechanism (eq 1, route A) that “plausible under some, but not all, of the conditions used is hydrolysis via protonation of the alkene’’ (eq 1, route B). From studies on the hydrolysis of a-bromo-p-aminostyrene (la) in aqueous buffers and perchloric acid they concluded that for l a “the vinyl carbonium ion mechanism for this compound is definitely incorrect and that hydrolysis most probably occurs via acid catalyzed hydration.”’ For compounds having a trans-hydrogen atom at the double bond in respect to the leaving group X a third mechanism must be considered. In this mechanism, (1) W. M. Schubert and G . W. Barfknecht, J . Amer. Chem. SOC.,92, 207 (1970).
especially under neutral or alkaline conditions, the corresponding acetylene beside route A can also be formed by a concerted elimination of HX (route C). In contrast an acetylene formation is not possible via route B. Table I shows predictions for reaction via
R,
SOH
;c=c
X
Q
8‘Rs --HX
R1\
/b
so’
‘
X-C-C-H
R3
Rl-CzC-R#
1, Ri = YCeH4; Rz = R3 = l a , Y = p - N H 2 ; X = Br l b , Y = p-MeO; X = Br
H
IC.Y = H: X = OS0,Ar - -----21R; = A&; Rz = Arz; R3 = Art; X = C1, Br, I, OSOZAr, OSOzF, OSOzCFa I
~~
3,R1= Arl; Rz = Ar2; R3 = ArS; X
= OSOzAr
4,R1 = CH:CMez; Rz = R3 = H or Me; X = Br 5. R l = Rz = Me: RI = H : X = OSOoAr. - , OSOXF, ~ _ ” ~
6 ; R; = R; = Ph;’ R3= morpholyl; X = C1, Br 7,R1 = cyclopropyl; RZ = R a = H ; X = C1, I 8,R1 = R3 = Me; RZ = H ; X = OSOZAr, OS02CF3 9, R1 = cyclopropyl; X = I 9a, Rz = Me; R3 = H 9b, Rz = H ; R3 = Me 10,Ar-CX:C:CPhz; X = C1 ll,R1= Me; RZ = R3 = Ph; X = OS02CF3 12,R1 = t-Bu; Rz Rt = H; X = OSOzCFI
.
the electrophilic addition-elimination route (for both Markovnikov and anti-Markovnikov additions) or via the vinyl cation intermediate, for 20 different phenomena. The experimental data for the systems 1-12 so far investigated are given in the last two columns. It is clear that the data are compatible only with the sN1 route, except for reactions of 5 in HCOOH,2 of l a in acidic media, and of l b in unbuffered AcOH. In the latter three cases the addition-elimination route was already suggested and it is significant that the same substrates in nonacid media (i.e., 5 in MeOHH20,4 l a in 80% EtOH,5 and l b in buffered AcOH3) react (according to Table I) only uia route A. As an example of a concerted elimination (route C) in nonacidic solvent compound 8 shall be given. Besides route C, route A can be made responsible for the acetylene formation; examples are IC, 4, 5, 7; in the case of 9 the acetylene formation can only be explained through route A. While l a solvolyzes in acidic media via additionelimination, extrapolation to pH of Schubert’s kobsd datal in water gives k50” = 1.4 IO-’ sec-l (and lower values at higher pH), by using Grob’s data5 kI5O0= 0.035 sec-l in basic 80% ethanol. The difference of at least five orders of magnitude in rate is a real discrepancy, which at present is difficult to explain.6 (2) See Table I, footnote 00.
(3) See Table I, footnote aa. (4) See Table I, footnote u. ( 5 ) See Table I, footnote p .
(6) This difference is even higher if account is taken of the difference in the two solvents. It was suggested by Professor W. M. Schubert
(private communication) that this is due to formation of sufficient amount of unneutralized protons, so that Grob’s data really reflect addition mechanism by these protons. On the other hand, Schubert and Barfknechtl did not consider the possibility of electrophilic acceleration of the solvolysis by protons, uiu protonation on the bromine, which should contribute to SN1 solvolysis even under acidic conditions.
Communications to the Editor
